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Numerical-Valued Fourier Transforms

Published online by Cambridge University Press:  20 November 2018

Raimond A. Struble
Raimond A. Struble*
Affiliation:
Department of Mathematics, North Carolina State University Raleigh, North Carolina27607
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Abstract

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It is shown that the classical Fourier transform can be extended as an algebra isomorphism onto the algebra of all complex-valued functions, which are measurable and finite a.e., under pointwise addition and multiplication. The extended Fourier transform agrees with the distributional Fourier transform on the space of all distributions which have regular transforms. It is defined on an algebra of Mikusiński-type operators in which multiplication is convolution in the subspace of integrable distributions.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 1 , 01 March 1977 , pp. 125 - 127
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Price, B., On the Laplace transforms for distributions, SIAM J. Math. Anal. 6 (1975), 49-80.Google Scholar
2. Struble, R. A., Representations of Fourier transforms for distributions, Bull. Inst. Acad. Sinica 2 (1974), 191-206.Google Scholar
3. Struble, R. A., The numerical-valued Fourier transform in the two-sided operational calculus, SIAM J. Math. Anal. (1977), 243-257.Google Scholar